with a suitable constant \(c_{d,\sigma }>0\) ; see e.g. [1]}. This pointwise formula does actually make sense for a larger class of functions,
e.g. when \(f\in L_1(dy/(1+|y|)^{d+2\sigma })\)  and \(f\)  is Hölder continuous of order \(2\sigma +{\varepsilon }\)  near the point \(x\) .
For general operators \(L\) , however, explicit expressions such as (REF ) are not common, and
the definition of \(L^\sigma f\)  as in (REF )-(REF ) must necessarily be restricted to a suitable
dense class of functions \(f\) .
